Gordon Brown today brushed off the latest attempt to oust him as prime minister as "a storm in a teacup" and insisted his cabinet was fully behind him, despite lukewarm statements of support issued by some of his top team late yesterday.

The prime minister spoke out as he faced opposition calls for an immediate general election following an attempt by two former cabinet ministers to unseat him.

In a concerted exercise to draw a line under the affair, Brown's spokesman briefed that the prime minister retained "the full confidence" of his entire cabinet while Brown himself used the airwaves to make light of an email sent to the Labour parliamentary party yesterday calling for a secret ballot to settle "once and for all" the divided issue of his leadership.

In his first remarks since the botched attempt at a coup by his former chief whip, Geoff Hoon, and Patricia Hewitt, a former health secretary, the prime minister insisted he had spent little time considering the challenge to his leadership.

Brown told BBC Radio Solent: "It's taken up very little of my time. I think it's one of these sidelines in this time when people are far more worried about ... what we are doing to deal with the weather and to make sure that people are safe and secure. So it's not going to take up much of my time and hasn't, certainly, taken up much of my time."

He dismissed suggestions that ministers' eventual statements of support had been lukewarm, insisting: "You can read into quotes what you want."

Brown claimed that most cabinet ministers demonstrated their support for him "within an hour or two". "I would say to you this is a bit of a storm in a teacup. We are actually dealing with real storms at the moment."

He would continue to "lead from the front", he said, and "say what I think, even if sometimes it's unpopular".

Earlier, Jack Straw, the justice secretary, said the attempted coup had "sunk" and predicted that would unite the party.

But both David Cameron, the Conservative leader, and Nick Clegg, his Liberal Democrat counterpart, pounced on yesterday's events as proof that Labour was no longer fit to govern.

The prime minister fought for several hours yesterday afternoon to shore up his authority, culminating in David Miliband – the man seen by many within the party as his potential successor – issuing the most equivocal statement of all the cabinet's comments.

It said: "I am working closely with the prime minister on foreign policy issues and support the re-election campaign for a Labour government that he is leading."

Miliband's statement came seven hours after Hewitt and Hoon tried to stir cabinet discontent with Brown's leadership into an open rebellion.

A phalanx of key cabinet ministers eventually rallied to Brown's standard during the course of the afternoon, including Alan Johnson, Harriet Harman, Alistair Darling and Lord Mandelson.

Cameron told BBC Radio 4's Today programme this morning: "If ever there was a time when our country needed strong leadership and a united government, it's today. We've got this massive budget deficit, we are at war in Afghanistan, we have got deep social problems, and yet we have got a government completely divided.

"If ... the prime minister does not really have the support of his senior colleagues, people will ask: 'Why should anyone else support him?' You just have to ask yourself: 'How much time do you think senior ministers were spending yesterday thinking about the budget deficit, about the education of our children, about the war in Afghanistan, and how much were they thinking about their own futures and their own careers?' for you to realise ... that we cannot go on like this. We have got to have an election and a change of government."

Meanwhile Clegg told GMTV that the failed coup showed why the country needed a general election. "The Labour party now is more interested in talking about itself," the Lib Dem leader said.

Commenting on yesterday's events, Straw, who ran Brown's Labour leadership bid when he succeeded Tony Blair in 2007, said the "ill-judged and very ill-advised" email would only serve to unite the party.

He said he did not believe the party was still divided over Brown, adding: "I actually think it will have the effect of bringing people behind his leadership even more."

"The party has reached a settled view. They want Gordon Brown to lead the party as prime minister into the general election whenever it takes place and they don't want to open the question of the leadership," the business secretary said.

Brown met many members of his cabinet before they issued their pledges of loyalty, which were offered with varying degrees of enthusiasm. But Miliband, the figure most likely to succeed Brown, maintained a sonorous silence for hours after Hoon and Hewitt raised the flag of rebellion.

The foreign secretary's allies are understood to have sent emissaries to contact the rebels to say they believed he would act if there were clearer signs that the rebellion was spreading across the parliamentary party.

Last night, the BBC said they understood six cabinet ministers had signalled they would have supported a further move against Brown, while former defence minister Eric Joyce wrote on his blog that to his knowledge two cabinet minsters had promised they would act, but had not.

By yesterday evening, though, Hoon admitted that the attempt to force a ballot appeared to have failed.

"I accept that we have set out that opportunity [to resolve the leadership issue] that Labour MPs by and large have not taken," he told the BBC's Newsnight programme.

When asked by presenter Jeremy Paxman, "if you were Brutus, Caesar would have been fine, wouldn't he?" Hoon agreed.

The frenzied activity was triggered at lunchtime when Hoon and Hewitt – in a coordinated move in which they emailed all Labour MPs – called for a secret ballot to decide once and for all if Brown should lead the party into the election.

Many Labour MPs said they were disgusted with the former chief whip Hoon and said he had taken leave of his senses. Even some sympathetic to the move questioned the lack of preparation and the timing.

In their letter, the rebels wrote: "Many colleagues have expressed their frustration at the way in which this question is affecting our political performance. We have therefore come to the conclusion that the only way to resolve this issue would be to allow every member to express their views in a secret ballot."

But they made their move only minutes after Brown had given one of his most effective performances at prime minister's questions and hours after Mandelson had used a speech on growth to mark the end of his temporary disillusionment with Brown's premiership.

The rebels felt compelled to move now, believing this was their last chance to oust the prime minister before the general election.

Unlike the serious push last summer, involving many backbench MPs and culminating in the resignation of the work and pensions secretary, James Purnell, this month's plotters focused their hopes on igniting a rebellion among a group of seven or so cabinet ministers.

Few backbench MPs – apart from some serial rebels – came out in support of the move.

The letter, which Hoon finalised with Hewitt's approval late on Tuesday night, warned: "This is a clear opportunity to finally lay this matter to rest. The continued speculation and uncertainty is allowing our opponents to portray us as dispirited and disunited. It is damaging our ability to set out our strong case to the electorate. It is giving our political opponents an easy target."

Hoon and Hewitt claimed they were simply calling for a ballot that critics and supporters of the prime minister should have no difficulty in supporting because it would allow the party to unite, whatever the result.

They wrote: "There is a risk that the persistent background briefing and grumbling could continue up to and possibly through the election campaign, affecting our ability to concentrate all of our energies on getting our real message across."

The letter prompted the most serious Downing Street rescue operation for the prime minister since Purnell's resignation.

As the day wore on, the focus moved to the strength of support being given by other cabinet ministers known to be uneasy about Brown's leadership skills.